This currently does not work because, in this case,
the morphism is just in the category of commutative
additive groups (i.e. the intersection of the
categories of modules over \(\ZZ\) and over \(\QQ\)):

side – ‘left’ or ‘right’ (default: ‘right’):
on which side of self the elements of \(S\) acts.

See annihilator() for the assumptions and definition
of the annihilator.

EXAMPLES:

By default, the action is the standard \(*\) operation. So
our first example is about an algebra:

sage: F=FiniteDimensionalAlgebrasWithBasis(QQ).example();FAn example of a finite dimensional algebra with basis:the path algebra of the Kronecker quiver(containing the arrows a:x->y and b:x->y) over Rational Fieldsage: x,y,a,b=F.basis()

In this algebra, multiplication on the right by \(x\)
annihilates all basis elements but \(x\):

sage: x*x,y*x,a*x,b*x(x, 0, 0, 0)

So the annihilator is the subspace spanned by \(y\), \(a\), and \(b\):

At this point, this only supports quotients by free
submodules admitting a basis in unitriangular echelon
form. In this case, the quotient is also a free
module, with a basis consisting of the retract of a
subset of the basis of self.